The Republican plan to avert the "fiscal cliff" that the White House rejected Monday includes at least one element that's likely to produce controversy: a proposal that would, among other things, affect the cost of living adjustment for Social Security.

"The basic argument is that the current annual inflation adjustment for Social Security and some other federal benefits overstates the true impact of inflation," NPR economics correspondent John Ydstie tells Audie Cornish, host of All Things Considered. "So, people are actually getting a bigger adjustment than they should."

Cost of living adjustments, which were added to Social Security in 1975, are based on inflation as measured by the Consumer Price Index, which measures the cost of a basket of goods. But many economists believe the CPI overstates the effect of inflation and prefer a different index, the chain CPI, which takes into account the substitutions that people make when prices rise.

"Let's say the price of beef goes up a lot," Ydstie says. "What people do is eat less beef and maybe more chicken, to keep their cost of living down. The current CPI doesn't account for those substitutions very well, and the chained CPI does. So, it measures inflation more accurately."

The switch by consumers to cheaper alternatives shaves about a quarter of a percentage point from the rise in their cost of living. Although annual changes aren't large, over a long period they compound into significant numbers.

Ydstie offers an example of someone earning $1,000 annually from Social Security. If inflation under the current measure was 2 percent last year, he says, that person's Social Security payment next year would be $1,020.

"But, under the new chained CPI, your benefit next year would be $1,017 a month — $3 less. Not a lot," he says. "However, let's say you live a long time, say 25 years on Social Security, the effects would compound and reduce your benefit by almost 10 percent."

The proposal has been criticized by congressional Democrats as well as seniors' groups like AARP, which argues that the chained CPI actually underestimates inflation costs for seniors, who spend more on health care than average Americans. Health care costs rise faster than average inflation.

Despite the opposition, however, this element of the plan could be part of getting to a compromise over averting the fiscal cliff, a combination of major tax increases and drastic spending cuts scheduled for the end of the year.

"The idea was on the table when President Obama and House Speaker Boehner were negotiating over a grand bargain last year," Ydstie says. "And it does provide a good deal of deficit reduction — around $200 billion over 10 years."

Half of that figure comes from smaller Social Security benefits, but an additional $50 billion comes from added tax revenues because it affects inflation adjustments in the tax code, too.

"That's part of its appeal because it brings in more tax revenues and reduces Social Security spending," Ydstie says. "It requires sacrifice from both Republicans and Democrats, but also gets each side something they want."